Just after becoming the culture secretary last week, Jeremy Hunt was asked what his priorities would be. He looked surprised and said that the first thing he had asked the department's civil servants to do was to work out how to help meet the £6bn of public sector savings required. Cuts of about £66m are expected in a newly reintegrated department, which gives Hunt responsibility for the Olympics as well as oversight of sport, media and the arts.

Yet, while the subsequent headlines focused on his comments that Olympics funding was not automatically protected, there are many more questions to answer. With such pressure to cut the deficit, it is unlikely that the Department for Culture, Olympics, Media and Sport will be high on the new coalition's agenda. It is still unclear how the Tory-led team will approach media issues in coalition with their Lib Dem partners, who perhaps significantly failed to join the departmental team.

Hunt was tantalisingly silent on the issue of his media policy ambitions following his appointment and there is also little to go on from the joint coalition manifesto, beyond a firm commitment, endorsed by all parties, to reform libel law. One adviser indicated last week that policies and a timetable for the implementation will have to be gone through, line by line. But if we take the pre-election statements as a guide there is common ground but also significant differences between the parties.

As shadow culture secretary, Hunt was notably hawkish on the BBC, keen on a deregulatory regime for commercial television, while showing a real dislike of a public subsidy for local TV news pilots and, along with other senior Tories, Ofcom's policy-making power. Will these views translate into the new administration?

The BBC

The Tory election manifesto promised to "support a strong and independent BBC that continues to make great content", yet the party has made no secret of its desire to reduce the size and scope of the corporation. Over the five-year life of the parliament it seems fair to say that the BBC faces major challenges – the level of the licence fee is up for negotiation from 2011/12. A Cameron proposal to freeze the licence fee, instead of waving through an agreed annual rise, was defeated by parliament last year.

The Conservatives and the Liberal Democrats share a view that the BBC's finances require external scrutiny by the National Audit Office. The NAO is overseen by the hawkish Public Accounts Committee, which is composed of several MPs who view the licence fee as a tax.

The cabinet's decision to cut members' own pay by 5% is a signal that executive pay scales are a target. The BBC Executive's strategic plan, Putting Quality First, puts the case for limited reform with cuts to BBC Worldwide and overall budgets. Consultation ends on 25 May, with the BBC Trust chairman, Sir Michael Lyons, due to make a statement on 30 June.

Likelihood of an attempt to freeze the licence fee: 8/10

The BBC Trust

Neither party supports the BBC Trust, the governance body created by Labour in 2007, which is both the corporation's regulator and its champion.

Hunt wants to create a licence fee payers' trust. As the Lib Dems also favour some form of external public service regulator, the trust's days look numbered. The issue is what can be done within the terms of the existing BBC charter, which runs until the end of 2016. Anything else could provoke a charge of overtly political interference in the governance of the BBC.

Halfway house changes could include a new role for a non-executive chairman to run the BBC executive board, alongside the director general, Mark Thompson. A trigger may be the deadline on whether to renew Lyons's appointment after April 2011.

Likelihood of action on the BBC Trust: 9/10

Ofcom

This was the ultimate New Labour creation in 2003 and the regulator is likely to lose some of its policy-making powers under a Lib-Con coalition. Broadcasting policy is now likely to originate in the DCOMS. Ofcom has already adopted a lower profile during the past year under its chair, Colette Bowe, with less frequent press conferences and speeches by its former No 10 policy adviser, Ed Richards.

Ofcom's ruling that BSkyB cuts its wholesale prices for premium sports and movie channels is subject to appeal to the Competition Appeals Tribunal, and the new government is unlikely to want to wade into such a politically charged area. Hunt said on 31 March that: "Competition issues should be decided at arm's length of government, which is why we support an independent Ofcom."

The Digital Economy Act, passed in April, allows Ofcom to introduce lightertouch regulation across radio and commercial television, which would allow the commercial broadcasting sector to operate more freely, and lessen the public service broadcasters' burdens. Ofcom has already moved to allow more regional hubs for local commercial radio, relax local programming quotas, and encourage digital stations. It is also consulting on allowing commercial broadcasters to decide whether or not to sell all their advertising airtime. The new government is not expected to change rules on taste and decency, increase advertising minutes, or drop impartiality, and one flashpoint, restricted product placement in programming, was agreed under Labour.

Likelihood of Ofcom being abolished: 2/10

Commercial TV

ITV's shares have risen since the election, partly because the fate of commercial television is thought to be very close to the heart of Cameron, who once worked at Carlton TV. Ed Vaizey, the new culture minister, told the annual ISBA conference of advertisers that "we are extremely keen to deregulate the broadcasting industry". Hunt suggested on the same day in the Financial Times that government could use override powers in the 1978 Interpretation Act to usher out the Contract Rights Renewal system. The Conservatives and Lib Dems have both supported the ending of CRR.

However, last week the Competition Commission confirmed its decision that the system should stay, but suggested a full review of the television advertising sales market. Both parties are firm supporters of Channel 4, which has dropped its pleas for public support.

Likelihood that commercial broadcasting will be deregulated: 10/10

Local media

The potential for a real clash. The Lib Dems were strong supporters of IFNCs, (independently financed local news consortia), a red line to Hunt. Up for debate must be any future sharing, or top slicing of the licence fee, but the Conservative instinct is to dispense with subsidy.

ITV chairman Archie Norman, who is close to the Tory party, is thought to have offered a deal: if ITV is given a more relaxed regulatory remit it will consider a U-turn and reinvest in both national and regional news. The Conservatives also favour reforming the rules relating to local media enterprises, with a view to allowing local newspapers to merge and establish "cross-platform networks" to protect their commercial viability.

Hunt is a passionate advocate of local city television, and has been advised by YouGov chairman Roger Parry on how to encourage commercially viable local television networks, not just through relaxing media ownership rules, but also by innovation in raising revenue.

Likelihood of subsidised local news pilots: 0/10

With the Olympics likely to take up much of Hunt's time, it may be left to Vaizey to march into other areas. On 6 May, he tweeted his relief that he had remained gaffe-free during the month-long campaign period. It remains to be seen how long that lasts.